Okay, here's another approach to the original location problem. It's fairly direct, but it needs a humorous presentational ploy to make the actions seem natural:
Spread for selection, hopefully near center, and use LJ Immediate Bottom Placement (crediting dispute aside, I happen to like the details of this handling the best) to leave selection apparently out-jogged and actual selection on bottom of deck.
Say: "I leave it sticking out for a simple reason: that way, I'll always know where it is: it's the one card sticking out." Spread deck as you say this, sight count 7 cards from bottom and square up with break above those 7 cards. Cant the out-jogged card to the L a little. Continue: "Even if the deck gets cut, I can't miss it." As you say this line, do the following three-packet cut to table: Cut about 1/3 to table (cutting above out-jogged card for sure), cut all the cards above the break (with the out-jogged card sticking out of this packet) on top of the tabled pile, and then drop the remaining 7 cards on top. "Just kidding! I wouldn't play you like that," or something like that. Square the in-jogged card and you're set.
If you start with a card crimped seventh from the bottom of deck, or in-jogged seventh from the bottom, you can do the control and then immediately go into the cut without spreading/sight-counting first.
Basically a pass-less (and therefore less direct) version of Kevin Baker's second solution above.